Problem 1:
While driving on a country road at a constant speed of 15.0 m/s, you encounter a dip in the road. The dip can be approximated by a circular arc with a radius of 75.0 m. What is the normal force exerted by the car seat on a 70 kg passenger at the bottom of the dip? Hint: Draw first a free body diagram that shows all the forces acting on the passenger, then apply Newton's second law.
Problem 2:
A centrifuge is a laboratory device used in Chemistry, biology, and medicine for increasing the sedimentation rate and separation of a sample by subjecting it to a very high centripetal acceleration.
A centrifuge rotates at a rate such that the bottom of a test tube travels at a speed of 93.8 m/s. The bottom of the test tube is 5.80 cm from the axis of rotation. What is the centripetal acceleration at the bottom of the test tube in m/s? Take g = 9.81 m/s.
Problem 3:
An energetic father places his 30 kg child in a 5.0 kg cart to which is attached a 2.0 m long rope. He then holds the end of the rope and spins the cart and child in a circle, keeping the rope parallel to the ground. If the tension in the rope is 100 N, how many revolutions per minute does the cart make? Hint: Draw first a free body diagram that shows all the forces acting on the passenger, then apply Newton's second law.
Problem 4:
If the road is banked at the proper angle θ, a car can round a curve without the assistance of friction between the tires and the road and without skidding.
What bank angle θ is needed for a 10,000 kg car traveling at 50.2 m/s around a curve of radius 58.0 m?
Now, change the speed of the car to 25.0 m/s and calculate the bank angle.
What observation do you make regarding the bank angle when the speed of the car is 25.0 m/s compared to 50.2 m/s?
Problem 5:
Two tugboats push on a barge at different angles (see figure below). The first tugboat exerts a force of 7.2x10^5 N in the x-direction, and the second tugboat exerts a force of 3.6x10^5 N in the y-direction. The mass of the barge is 5.0x10^6 kg and its acceleration is observed to be 5.7x10^-2 m/s^2 in the direction shown in the figure below. What is the drag force of the water on the barge resisting the motion? Hint: Drag force is a type of frictional force.
Problem 6:
A mass of 5 kg is suspended by a rope of length 2 m from the ceiling. A force of 54 N in the horizontal direction is applied at the midpoint (call it R) of the rope. What is the angle the rope makes with the vertical in equilibrium (i.e. when Newton's first law applies)? Take g = 9.81 m/s^2, and neglect the mass of the rope.