Help Me Ace My Physics Final: Solving 12 Difficult Problems

[Caldus]

My final exam for Physics is tommorrow and I'm just not good with this stuff at all.

Here are some problems that I'm having trouble with on this review worksheet I was given. I don't need answers, I need to know how to do these problems. If anyone could show me how to do at least a problem or two then I would greatly appreciate it:

1. A pilot heads due north at an air speed of 380 km/h. A 112 km/h wind is blowing from the west. Calculate the velocity of the plane relative to the ground. (I just don't know how to convert from km/h to m/s.)

2. An object is shot up into the air at a 45 degree angle with a velocity of 141 m/s. Calculate the distance the object travels before striking the ground.

3. An astronaut weighs 900 N at the Earth's surface. Calculate the astronaut's weight at an altitude of 32,000 km above the Earth's surface.

4. A 5.0 g bullet leaves a gun at 1.00 x 10^3 m/s. The gun has a mass of 4.0 kg. Calculate the recoil velocity of the gun.

5. A 2.85 x 10^5 N freight car coasts along a level track at 1.2 m/s. The brakes are applied, and the car stops in a distance of 6.0 m. Calculate the average braking force.

6. What is the kinetic energy of a 15,700 N car moving at 30 km/h?

7. A 6.0 kg ball is at rest at the top of an inclined plane that is 2.5 m tall. What is the speed of the ball when it reaches the bottom of the incline?

8. A track star in the broad jump goes into the jump at 12.0 m/s and launches himself at 20.0 degrees above the horizontal. How far does he jump?

9. An object that weighs 5000 N is suspended by two cables. Cable 1 applies a horizontal force to the right of the object and has a tension T1. Cable 2 applies a force upward and to the left at an angle of 37 degrees with the horizontal and has a tension T2. Determine the magnitude of T1 and T2.

10. Determine the acceleration of a 25 kg crate that is pulled across the floor by a 275 N force applied at 35 degrees above the horizontal. The frictional force is 15 N.

11. What upward force is applied by a crane to lift a 2200 kg car at a constant velocity of 5 m/s.

12. What upward force is applied by a crane to lift a 2200 kg car at a constant upward acceleration of 5.0 m/s^2?

Again, I'm not looking for someone to do all of these, but at least a few maybe so that I may be able to figure out other problems.

Thanks.

 

[BoulderHead]

Greetings Caldus, and welcome to PF !

Again, I'm not looking for someone to do all of these, but at least a few maybe so that I may be able to figure out other problems.

How about if you’re given a few tips that help you to solve them yourself? Here are a couple of hints;

1) 1 km = 1000 meters. 1 hour = 3600 seconds. 1km/hr = 1000m/3600s.

2) Do you know how to break this down into the X and Y components?

Does that help any?

 

[KLscilevothma]

Originally posted by Caldus
2. An object is shot up into the air at a 45 degree angle with a velocity of 141 m/s. Calculate the distance the object travels before striking the ground.

The object will undergo projectile motion. As BoulderHead has said, we need to break this down into the X and Y components.

Let u be the initial velocity (141 m/s in this case)
θ be the angle of projection (45 degrees in this case)

Take upward positive
For X component, the horizontal motion :
initial velocity, u_x = u cos θ = 141 cos θ
distance traveled in time, t = utcosθ
acceleration = 0 since there is no external force acting horizontally on the object.

For Y component, we can apply Newton's laws of motion because the object is under constant acceleration, which is gravity, g.
acceleration, a= -g
initial velocity, u_y = u sin θ
velocity after time t, v_y = usin θ -gt
displacement, s_y = ut sin θ - 0.5 gt²

When the object reaches the ground again after the projectile motion, vertical displacement, s_y = 0
therefore
ut sin θ - 0.5 gt² = 0
t = 2u sin θ / g .......(1)

Horizontal displacement
= ut cos θ .....(2)

substitute (1) in (2), you'll get the answer.

 

[KLscilevothma]

3. An astronaut weighs 900 N at the Earth's surface. Calculate the astronaut's weight at an altitude of 32,000 km above the Earth's surface.

Gravitational field strength, g = GM/r^2, where r (unit : meter) is the distance between the centre of the Earth and the astromaut, which is radius of the Earth + height from the ground. M is the mass of the Earth and unit is kg.
Weight of the astronaut = mass*g

Moreover, you can find out the gravitational field strength at any altitude above the Earth by that formula, but don't forget to add the radius of the Earth to the height above the ground.

4. A 5.0 g bullet leaves a gun at 1.00 x 10^3 m/s. The gun has a mass of 4.0 kg. Calculate the recoil velocity of the gun.

Use conservation of momentum.
[sum] m_iv_i = [sum]m_jv_j
In this case, momentum before the bullet leaves the gun = 0.
Momentum after the bullet leave the gun = m_gun*v_gun+m_bullet*v_bullet
Therefore,
m_gun*v_gun+m_bullet*v_bullet=0

11. What upward force is applied by a crane to lift a 2200 kg car at a constant velocity of 5 m/s.

Since the car is lifted with constant velocity, meaning no external force is acting on it. Therefore weight of the car = force applied by the crane = mg

12. What upward force is applied by a crane to lift a 2200 kg car at a constant upward acceleration of 5.0 m/s^2?

[sum] F = ma
Force applied by the crane - weight of the car = mass of the car * acceleration.
F - mg = ma