What Formulas Should I Use for These Challenging Physics Problems?

[stumillardkm]

I have a couple problems for my physics class that I am needing help with: (and not sure which formulas to use)
1. A 1050 kg car has a maximum power output of 150 hp. How steep a hill can it climb at a constant speed of 70 km/h if the frictional forces add up to 700N?

2. A vertical spring (ignore its mass) with a spring constant 1000 N/m is attached to a table and is compressed 0.250 m (vertically).
a. This spring is used to launch a .200 kg ball. What will the speed of the ball be when it leaves the spring?
b. How hgh above it's original position (spring compressed) wil the ball fly?

3. Designers of todays cars have built "5 mph (8 km/hr) bumpers" that are designed to elsatically compress and reboudn withoug any physical damage at seeds below 5 mph/8km/hr. IF the material of the bumpers permanently deforms after a copression of 1.5 cm, but remains like an elastic spring up to that point, what must het effective spring constant of the bumper material be? Assume the car has a mass of 1600 kg and is tested to ramming into a solid wall.


For #3, I'm thinking that i have to use the PE= 1/2 kx^2 formula for the elastic potential, but the mass is throwing me off.

For #2, I am just lost - want to use the same formula as above, but don't know what to plug in or if I'm using the right one at all!

For #1, I'm not sure where to start - the power eq: work/time makes sense, but then the height? AUGH

Any help would be great!
Thanks

 

[Doc Al]

Originally posted by stumillardkm
For #3, I'm thinking that i have to use the PE= 1/2 kx^2 formula for the elastic potential, but the mass is throwing me off.

You are on the right track. Use conservation of energy. Do it right, and the mass will drop out.

For #2, I am just lost - want to use the same formula as above, but don't know what to plug in or if I'm using the right one at all!

Once again, conservation of energy. You have spring PE, gravitational PE, and KE.

For #1, I'm not sure where to start - the power eq: work/time makes sense, but then the height?

The car's energy goes into two things: raising the car (gravitational PE) and overcoming friction (work done against friction). And yes, power = energy/time.

 

[M98Ranger]

For problem #1, you can use the power equation P = Fv, where P is power, F is force, and v is velocity. In this case, the force is the sum of the frictional forces and the weight of the car (mg), and the velocity is 70 km/h converted to m/s. You can then use the equation P = mgh/t to solve for the height (h) of the hill, where m is the mass of the car, g is the acceleration due to gravity, and t is the time it takes to climb the hill at a constant speed. You can then use trigonometry to find the angle of the hill.

For problem #2, you can use the equation for elastic potential energy, PE = 1/2kx^2, where k is the spring constant and x is the compression distance. To find the speed of the ball, you can use the conservation of energy principle, where the elastic potential energy is converted to kinetic energy (KE = 1/2mv^2). To find the height, you can use the equation for projectile motion, h = v^2sin^2(theta)/2g, where v is the initial velocity, theta is the angle of projection, and g is the acceleration due to gravity.

For problem #3, you can use the equation for elastic potential energy again, but in this case, the force is the weight of the car and the displacement is the compression distance of the bumper. You can then equate this to the work done by the car, which is equal to the change in kinetic energy (KE = 1/2mv^2). You can then solve for the effective spring constant (k) using the equation KE = 1/2kx^2. The mass of the car is given, so you can plug that in as well.