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4. Ball A rotates without friction on the end of a 30cm rod. Cart B rolls freely in the horizontal direction. Initially Cart B is a rest, and Ball A is released from rest with the rod horizontal. When the ball gets to the bottom of its swing, it impacts Cart B. After impact the Ball rebounds to 30°. What is the speed of Cart B just after impact, v_{B3} = ? State 1 Ball A released from rest v_{A1} = 0 v_{B1} = 0 State 2 Just before impact v_{A2} v_{B2} = 0 State 3 Just After Impact v_{A3} v_{B3} = ? State 4 speed of Ball A is zero m_A = 200 g m_B = 600 g R = 30 cm As usual in this part of the course, neglect the size of the ball and the mass of the rod. Hint: This problem is not as complicated as it might first appear. I made four drawings to help split it into events that need conservation of energy versus conservation of momentum. Be careful of the sign of v_A, and use correct value for gravity whether leaving it in cm-gram-sec system or changing to m-kg-sec system.

          4. Ball A rotates without friction on the end of a 30cm rod. Cart B rolls freely in the horizontal direction. Initially Cart B is a rest, and Ball A is released from rest with the rod horizontal. When the ball gets to the bottom of its swing, it impacts Cart B. After impact the Ball rebounds to 30°. What is the speed of Cart B just after impact, v_{B3} = ?

State 1
Ball A released from rest
v_{A1} = 0
v_{B1} = 0

State 2
Just before impact
v_{A2}
v_{B2} = 0

State 3
Just After Impact
v_{A3}
v_{B3} = ?

State 4
speed of Ball A is zero

m_A = 200 g
m_B = 600 g
R = 30 cm

As usual in this part of the course, neglect the size of the ball and the mass of the rod.

Hint: This problem is not as complicated as it might first appear. I made four drawings to help split it into events that need conservation of energy versus conservation of momentum. Be careful of the sign of v_A, and use correct value for gravity whether leaving it in cm-gram-sec system or changing to m-kg-sec system.

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4. Ball A rotates without friction on the end of a 30cm rod. Cart B rolls freely in the horizontal direction. Initially Cart B is a rest, and Ball A is released from rest with the rod horizontal. When the ball gets to the bottom of its swing, it impacts Cart B. After impact the Ball rebounds to 30°. What is the speed of Cart B just after impact, vB3 = ?

State 1
Ball A released from rest
vA1 = 0
vB1 = 0

State 2
Just before impact
vA2
vB2 = 0

State 3
Just After Impact
vA3
vB3 = ?

State 4
speed of Ball A is zero

mA = 200 g
mB = 600 g
R = 30 cm

As usual in this part of the course, neglect the size of the ball and the mass of the rod.

Hint: This problem is not as complicated as it might first appear. I made four drawings to help split it into events that need conservation of energy versus conservation of momentum. Be careful of the sign of vA, and use correct value for gravity whether leaving it in cm-gram-sec system or changing to m-kg-sec system.

Added by Cathy B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

05/27/2022

Step 1

Given: - Mass of Ball A, m = 200 g = 0.2 kg - Acceleration due to gravity, g = 9.8 m/s^2 - Length of the rod, R = 30 cm = 0.3 m Using conservation of energy: Potential energy before impact = Kinetic energy just before impact mgh = 0.5mv^2 0.2 * 9.8 * 0.3 = 0.5 * Show more…

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4. Ball A rotates without friction on the end of a 30cm rod. Cart B rolls freely in the horizontal direction. Initially Cart B is a rest, and Ball A is released from rest with the rod horizontal. When the ball gets to the bottom of its swing, it impacts Cart B. After impact the Ball rebounds to 30°. What is the speed of Cart B just after impact, v_{B3} = ? State 1 Ball A released from rest v_{A1} = 0 v_{B1} = 0 State 2 Just before impact v_{A2} v_{B2} = 0 State 3 Just After Impact v_{A3} v_{B3} = ? State 4 speed of Ball A is zero m_A = 200 g m_B = 600 g R = 30 cm As usual in this part of the course, neglect the size of the ball and the mass of the rod. Hint: This problem is not as complicated as it might first appear. I made four drawings to help split it into events that need conservation of energy versus conservation of momentum. Be careful of the sign of v_A, and use correct value for gravity whether leaving it in cm-gram-sec system or changing to m-kg-sec system.

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Transcript

00:01 It is given that bowl a, which is on the end of 30 cm of the road, bowl a, is released from rest to the road horizontal and it hits carp b.

00:16 Carp b, which was at rest initially.

00:21 So it is asked to calculate the speed of the cart after pollution.

00:27 Now first we can calculate the velocity of bowl before pollution, which is b, a, i.

00:32 Now initially all the energy is in the form of potential energy.

00:38 So this potential energy is converted into kinetic energy just before the impact.

00:44 So according to the conservation of energy before collision, we can write potential energy is equals to kinetic energy.

00:51 For potential energy is mgh and kinetic energy is half mv square or half m a i square, which is the velocity of volt before pollution.

01:04 Now from this we can obtain an expression for b -a -i which is equal to root of 2 g -h.

01:14 Now it is given that h which is equal to r the length of the road as 30 cm or this is equal to 0 .3 meters.

01:28 Now substitute this in the above expression we have b -a -i the velocity of bowl before pollution is equal to 2 into 9 .8 meter per second square into 0 .3 meter.

01:43 This will give a value of 2 .45 meter per second.

01:50 Now the final velocity of the ball after pollution, that is b b f, sorry b a f.

02:01 Now after the impact ball a rebounds to 30 degree.

02:05 That is the ball makes an angle 30 degree with a vertical.

02:08 I can just draw the figure.

02:11 So we have the vertical and the bowl is at an angle 30 degree with the vertical.

02:20 Angle 30 degree with the vertical.

02:23 So here we have ball a.

02:26 Now we have the total length of the road as r which is equal to 30 centimeters...

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