- What is the dot product between two vectors one of which is 15m in the northern direction and one of which is 20m long in a direction 30° south of east?
- What is the dot product of the two vector and ?
- Determine the angle between the two vectors in the previous example?
- A 40kg package slides down a ramp for 2.5m that makes an angle of 30° with the ground. How much work does the normal force do? How much work is done by gravity?
- Two people move a heavy crate of mass 300kg. One person pulls it straight up with a force of 1000N, the other pulls it in the horizontal direction with a force of 600N. If the crate moves 3.5m, how much work has each person done?
- You have a robotic arm that applies a force that goes like F(x) = 3x² – 8 x. What is the work this force does if applied from x=0 to x=0.5?
- What is the kinetic energy of a bullet with mass 4.2g and a velocity of 965 m/s? How about a 65kg person walking at 1.5m/s?
- What is the kinetic energy of a penny (mass of 2.5g) traveling at 12 m/s?
- How fast must you drive a car of mass 1500kg so that it has the same kinetic energy as a motorcycle of mass 300kg traveling at 15m/s?
- If you are on the 8th floor of a building and you go down to the 3rd floor and each floor is 3.5m high, what is the change in your potential energy?
- If you have a spring that when you attach a 600g mass to it the spring is stretched 8cm down what is the change in potential energy of the spring by this stretching?
- If a 65kg person visits the International Space Station, 400km above Earth’s surface, what is the change in their potential energy?
- If you get on a trampoline and the trampoline goes down 25cm, what is the change in your gravitational and elastic potential energy if the spring constant of the trampoline is k=400 N/m ?
Conservation of Energy
- If you use a canon to fire a 25kg canon ball straight up in the air and the canon ball leaves the canon with a velocity of 8m/s, how high will it go? Ignore friction.
- If you are at a water park and you get on a water slide that is 30m high, how fast will you be going when the slide reaches the ground if your mass is 50kg? Ignore friction.
- (a) Calculate the force needed to bring a 950-kg car to rest from a speed of 90.0 km/h in a distance of 120 m (a fairly typical distance for a non-panic stop). (b) Suppose instead the car hits a concrete abutment at full speed and is brought to a stop in 2.00 m. Calculate the force exerted on the car and compare it with the force found in part (a).
- Using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 20.0 m above water with an initial speed of 15.0 m/s strikes the water with a speed of 24.8 m/s independent of the direction thrown.
- (a) How high a hill can a car coast up (engine disengaged) if work done by friction is negligible and its initial speed is 110 km/h? (b) If, in actuality, a 750-kg car with an initial speed of 110 km/h is observed to coast up a hill to a height 22.0 m above its starting point, how much thermal energy was generated by friction? (c) What is the average force of friction if the hill has a slope 2.50º above the horizontal?
- On aircraft carriers elastic hooks are used to help fighter jets land on the short runways. If a fighter jet has a mass of 8000kg and it approaches the runway at a speed of 25m/s what does the spring constant of the elastic hook have to be if it has to stop the plane in 30m.
- If a 2kg meteoroid is held 30km above the surface of the Moon, what speed would it hit the Moon with if it was let go?
- How much must you stretch a rubber band of spring constant k=800N/m in order for it to shoot a 250g rock 5m into the air? Assume the rock leaves the rubber band when it returns to its unstretchted length and there is no air resistance.
An elastic band acts as a spring with k=1500N/m. If you put a stone of mass of 250g in the band and pull it back 30cm, how fast will the stone be going when the elastic band returns to its unstrechted location? If you measure the speed of the stone at that point and find it is only 2.5m/s what was the average frictional force on the stone during its journey of 30cm?
- If you pull a 40kg box up a 30º incline such that it moves at a constant velocity of 4.5m/s, how much power will that take?
- If a 1500kg car traveling at 15m/s runs into a tree that brings it to a complete stop in 2s, how much power is exerted by the tree?