Newton’s Laws – Review Packet · 4. A 2.00-kg aluminum block and a 6.00-kg copper block are connected by a light string over a frictionless pulley. They sit on a steel surface,

Newton’s Laws – Review Packet

1. A high diver of mass 70.0 kg jumps off a board 10.0 m above the water. If his

downward motion is stopped 2.00 s after he enters the water, what average upward force did the water exert on him?

2. A 0.400-kg object is swung in a vertical circular path on a string that is 0.50 m long. a. If its speed is 4.00 m/s at the top of the circle, what is the tension in the string

there?

b. What is the minimum speed that the object must be travelling at the top of the circle, to complete the circle (so the string does not collapse)?

3. A 2.00-kg block is placed on top of a 5.00-kg block as in the picture below. The coefficient of kinetic friction between the 5.00-kg block and the surface is 0.200. A horizontal force, F, is applied to the 5.00-kg block.

a. Draw a free-body diagram for each block.

b. Calculate the magnitude of the force necessary to pull both blocks to the right with an acceleration of 3.00 m/s2.

c. Find the minimum coefficient of static friction between the blocks such that the 2.00-kg block does not slip under an acceleration of 3.00 m/s2.

2.00$kg$

5.00$kg$

4. A 2.00-kg aluminum block and a 6.00-kg copper block are connected by a light string over a frictionless pulley. They sit on a steel surface, as shown below (The ramp makes and angle, θ = 30o, with the horizontal). The coefficient of static friction between two steel surfaces is 0.740 and coefficient of static friction between a steel surface and a copper surface is 0.530. If released, will they accelerate? __________________________________________ • If so, determine the acceleration and the tension in the string • If not, determine the sum of the magnitudes of the forces of friction acting on

the blocks.

2$kg$

6$kg$

5. Consider the three connected objects shown in the picture. The inclined plane makes an angle, θ, with the horizontal. If the inclined plane is frictionless, and the system is in equilibrium, find (in terms of m, g, and θ)

a. The mass, M.

b. The tensions, T1 and T2.

If the round hanging mass was replaced with a mass of 2M (double the original),

c. Find the acceleration of the objects.

T1$

M$2m$

m$T2$

6. A simple accelerometer is constructed by suspending a mass, m, from a string of length, L that is tied to the top of a cart. As the cart is accelerated, the string-mass system makes a constant angle, θ with the vertical.

a. Draw a free body diagram for the mass.

b. Assuming that the mass of the string is negligible compared with m, derive an expression for the cart’s acceleration in terms of θ and show that it is independent of the mass, m, and the length, L.

c. Determine the acceleration of the cart when θ = 23o.

7. Two masses, m1 = 3.00 kg and m2 = 5.00 kg are connected by a light string that passes over a frictionless pulley.

a. Draw free body diagrams for the masses.

b. Find the acceleration of the masses.

c. Find the tension in the string.

d. If started from rest, how far will the masses move in one second?

m1$m2$

8. An amusement park ride consists of a rotating circular platform 8.00 m in diameter from with 10.0 kg seats are suspended at the ends of 2.50 m massless chains. When the system rotates, the chains make an angle of 28o with the vertical.

a. What is the period of rotation?

b. Draw a free body diagram of a 40.0 kg child riding in a seat as it rotates with the period from part a, and find the angle that the chain makes with the vertical.

9. A civil engineer wishes to design a curved exit ramp for a highway in such a way that the car will not have to rely on friction to round the curve without skidding (for example, on an icy day). The designated speed is 13.4 m/s, and the radius of the curve is 50.0 m.

a. At what angle should the road be banked?

b. How fast can a car safely travel on this ramp on a dry day, when the coefficient of friction between the road and tires is µ = .47?