Forces and Newton’s Laws
For each problem you must:
1)List your variables
2)Draw a Free-Body Diagram
3)State if the object is in equilibrium or not
4)Write the appropriate equations for the situation and solve.
Object’s in Equilibrium
1)A man is holding above his head a barbell whose mass was 253 kg. His mass at the time was roughly 133 kg. What is the normal force on exerted on him? Ans: 3790 N
2)A typical elevator is moving up at a constant speed with 5 people each having a mass of 80.00 Kg. (Ignore the weight of the elevator) Find the tension in the elevator cable. Ans: 3,920 N
3)A large gorilla with a mass of 3.10 X 102 kg hangs from two vines, each of which makes an angle of 30.0°. Find the tension in each vine. Ans: FT=3.04x103 N
4)The net force exerted by a woodpecker’s head when its beak strikes the bark of a tree is 4.90 N, assuming that the bird’s head has a mass of 0.050kg. If the vertical component of the net force is 1.70N, a) find the horizontal component of the net force. Ans: F = 4.60 N b) find the net acceleration. Ans: 98.0 m/s2
Newton’s Second Law
1)What is the weight of a car with a 3000.0 Kg mass on the Earth? How about on the moon? (gmoon=1.64 m/s2) Ans:Fg,Earth = 29,430. N; Fg,Moon = 4,920.0 N
2)A racing driver survived acceleration from 48.1 m/s to a stop in a distance if 0.660 m. His mass is 70.0 kg. What is the average acceleration and force that he feels during this crash? Ans: a=1750 m/s2, F=123,000 N
3)A very thin rod can sustain a force of 57 N. Assume the rod is used to pull a block along a smooth horizontal surface. If the maximum force accelerates the block 0.25m/s2, find the mass of the block. If a second force of 24N is applied in the direction opposite the 57 N force, what would be the new acceleration of the block? m = 230 kg, a = 0.14 m/s2
4)A giant crane lifted a load with a mass of 2.232 X 106 kg. Find the force needed to lift the load with an acceleration of 0.10 m/s2. ANS: 2.2 X 107 N.
5)Suppose a crane lifts a net with 2.0 X 104 kg mass off the ground. The net is steadily accelerated from rest over an interval of 0.80 s until the net reaches a speed of 1.0 m/s. Calculate the tension in the cable. Ans: FT = 2.2 x 105N
6)A mass of 3.18x105kg is pulled with a horizontal force of 82,000 N. If the is an opposing force of 62,000 N, because of the wind, what is the net acceleration of the trailer? ANS: 6.3 X 10-2 m/s2.
Objects with Friction
1)A 120. kg sled is pulled across a parking lot. The coefficient of friction between the sled and the pavement is 0.540. What is the maximum force of friction on the sled? Ans: 648 N
2)A mass of 11.0 kg was pulled along with a horizontal force of 42.0 N. If the objects velocity is constant, what is the coefficient of friction between the object and ground? Ans:μ=0.389
3)A car accelerated from rest to 26.7m/s in 3.07 s on a level road. Cars accelerate because of the force of friction between the tires and the road. Calculate the coefficient of friction between the tires and the road. Ans:=0.886
4)A car with a force of the engine is 4.00 X 104 N. What is the force of friction on the car if she has the cruise control on and what is the weight of the car if the coefficient of friction is 0.56? Ans: 40,000 N and 71,000 N.
5)What minimum force is needed to pull a mass of 1.90x105 kg at a constant velocity horizontally if the coefficient of friction between the surface and the mass is 0.160? Ans: Fapp = 2.98 X 105 N
6)A mass of 1.89 X 105 kg is dragged horizontally to a new location. Given the magnitude of the acceleration is 0.120 m/s2 and the coefficient of friction is 0.100, calculate the magnitude of the applied force? Ans: Fapp = 2.08 X 105 N
Objects on an Incline
1)What would be the coefficient of kinetic friction if a sled and a rider travel down the hill with a net acceleration of 2.00 m/s2? Ans:μ=0.523
2)A speed of 25.6 m/s was reached after 6.60 seconds after going down slope with as 35.0° incline. Find the coefficient of friction between the grass and the Skis. Ans: μ=0.219
3)A mass of 2.50 X 103 kg slides down a ramp that has a 45.0° incline, and the coefficient of friction between is 0.597, what is the net force acting on the mass? What is the magnitude of the mass’s net acceleration? Ans: Fnet = 6.99 X 103 ; anet = 2.80 m/s2
4)A street has an angle of 48.0° with respect to the horizontal. Suppose a 10.0 kg trunk is placed on the street. Find the applied force needed to keep the trunk at rest if the coefficient of friction is 0.464. Ans: 7.30 N
5)A car with a mass of 3335 kg is moving down a 10.0° slope when the driver applies the brakes. The wheels stop rotating, and the car slides, accelerating at a rate of -6.00 m/s2. Calculate the force of friction acting on the car as it slows down, and determine from that the coefficient of kinetic friction. Ans: f=25700N μ=0.798