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PROBLEM 5 – SPRING WORLD [25 points] A block, of mass M = 0.50 kg, rests on a frictionless horizontal table so that it is in contact with a spring of negligible mass and spring constant k = 600 N/m. A toy dart, of mass m = 0.10 kg, is shot at the block with a speed vi = 15 m/s (as is shown in part (a) of the figure). a) [2 points] First consider the collision between the dart and the mass M. What kind of collision is this? What is the velocity of the dart and the mass M after the collision? The dart sticks to the block with a suction cup. As a result of the impact, the spring first compresses (as shown in part (b) of the figure). b) [3+2 point] What is the change of length of the spring as it is compressed from its initial length to its length at maximum compression? ii) At the instant when the block is momentarily at rest and the spring is at its maximum compression, is the acceleration of the block zero, directed to the right, or directed to the left? Explain why. After the spring has returned to its equilibrium position, the block and dart move away from the spring, traveling to the left with a speed vf along the table (as shown in part (c) of the figure). c) [5 points] What is the final speed vf of the block and attached dart? A child's game consists of a block that attaches to a table with a suction cup, a spring connected to that block, a ball, and a launching ramp. By compressing the spring, the child can launch the ball up the ramp. The spring has a spring constant k, the ball has a mass m, and the ramp rises a height h. The spring is compressed a distance d in order to launch the ball. When the ball leaves the launching ramp its velocity makes an angle ? with respect to the horizontal. d) [ 3 points] Assuming that friction and air resistance can be ignored for the purposes of this problem, describe the changes in the forms of energy in the system from the time the spring is compressed until the ball first hits the ground. e) [ 5 points] Calculate the vector velocity (x, y components, magnitude and direction) of the ball when it leaves the launching ramp. Be sure to specify your coordinate system. f) [ 5 points] The spring constant = 32 N/m, the spring's compression is 5 cm, the ball's mass is 20 grams, the height of the ramp is 10 cm, and the top of the table is 1 m above the floor. With what speed will the ball hit the floor? (Use g ~ 10 m/s².) {Hint: it is easier if you find the initial total energy of the ball when it is moving on the flat part of the table}

          PROBLEM 5 – SPRING WORLD [25 points]
A block, of mass M = 0.50 kg, rests on a frictionless horizontal table so that it is in contact with a spring of
negligible mass and spring constant k = 600 N/m. A toy dart, of mass m = 0.10
kg, is shot at the block with a speed vi = 15 m/s (as is shown in part (a) of the
figure).
a) [2 points] First consider the collision between the dart and the mass
M. What kind of collision is this? What is the velocity of the dart and
the mass M after the collision?
The dart sticks to the block with a suction cup. As a result of the impact, the
spring first compresses (as shown in part (b) of the figure).
b) [3+2 point] What is the change of length of the spring as it is
compressed from its initial length to its length at maximum
compression?
ii) At the instant when the block is momentarily at rest and the spring is at its maximum compression, is the
acceleration of the block zero, directed to the right, or directed to the left? Explain why.
After the spring has returned to its equilibrium position, the block and dart move away from the spring,
traveling to the left with a speed vf along the table (as shown in part (c) of the figure).
c) [5 points] What is the final speed vf of the block and attached dart?
A child's game consists of a block that attaches to a table with a suction cup, a spring connected to that block, a ball,
and a launching ramp. By compressing the spring, the child can launch the ball up the ramp.
The spring has a spring constant k, the ball has a mass m, and the ramp rises a height h. The spring is compressed a
distance d in order to launch the ball. When the ball leaves the launching ramp its velocity
makes an angle ? with respect to the horizontal.
d) [ 3 points] Assuming that friction and air resistance can be ignored for
the purposes of this problem, describe the changes in the forms of energy
in the system from the time the spring is compressed until the ball first
hits the ground.
e) [ 5 points] Calculate the vector velocity (x, y components, magnitude and direction) of the ball when it leaves
the launching ramp. Be sure to specify your coordinate system.
f) [ 5 points] The spring constant = 32 N/m, the spring's compression is 5 cm, the ball's mass is 20 grams, the
height of the ramp is 10 cm, and the top of the table is 1 m above the floor. With what speed will the ball hit
the floor? (Use g ~ 10 m/s².)
{Hint: it is easier if you find the initial total energy of the ball when it is moving on the flat part of the table}

PROBLEM 5 – SPRING WORLD [25 points]
A block, of mass M = 0.50 kg, rests on a frictionless horizontal table so that it is in contact with a spring of
negligible mass and spring constant k = 600 N/m. A toy dart, of mass m = 0.10
kg, is shot at the block with a speed vi = 15 m/s (as is shown in part (a) of the
figure).
a) [2 points] First consider the collision between the dart and the mass
M. What kind of collision is this? What is the velocity of the dart and
the mass M after the collision?
The dart sticks to the block with a suction cup. As a result of the impact, the
spring first compresses (as shown in part (b) of the figure).
b) [3+2 point] What is the change of length of the spring as it is
compressed from its initial length to its length at maximum
compression?
ii) At the instant when the block is momentarily at rest and the spring is at its maximum compression, is the
acceleration of the block zero, directed to the right, or directed to the left? Explain why.
After the spring has returned to its equilibrium position, the block and dart move away from the spring,
traveling to the left with a speed vf along the table (as shown in part (c) of the figure).
c) [5 points] What is the final speed vf of the block and attached dart?
A child's game consists of a block that attaches to a table with a suction cup, a spring connected to that block, a ball,
and a launching ramp. By compressing the spring, the child can launch the ball up the ramp.
The spring has a spring constant k, the ball has a mass m, and the ramp rises a height h. The spring is compressed a
distance d in order to launch the ball. When the ball leaves the launching ramp its velocity
makes an angle ? with respect to the horizontal.
d) [ 3 points] Assuming that friction and air resistance can be ignored for
the purposes of this problem, describe the changes in the forms of energy
in the system from the time the spring is compressed until the ball first
hits the ground.
e) [ 5 points] Calculate the vector velocity (x, y components, magnitude and direction) of the ball when it leaves
the launching ramp. Be sure to specify your coordinate system.
f) [ 5 points] The spring constant = 32 N/m, the spring's compression is 5 cm, the ball's mass is 20 grams, the
height of the ramp is 10 cm, and the top of the table is 1 m above the floor. With what speed will the ball hit
the floor? (Use g 10 m/s².)
Hint: it is easier if you find the initial total energy of the ball when it is moving on the flat part of the table

Added by Gloria S.

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