sorry i have about 5 questions on this homework packet that i just can't figure out.... hope you can help me
A bowling ball (mass = 7.2 kg, radius = 0.12 m) and a billiard ball (mass = 0.41 kg, radius = 0.028 m) may each be treated as uniform spheres. What is the magnitude of the maximum gravitational force that each can exert on the other?
Three uniform spheres are located at the corners of an equilateral triangle. Each side of the triangle has a length of 1.50 m. Two of the spheres have a mass of 3.20 kg each. The third sphere (mass unknown) is released from rest. Considering only the gravitational forces that the spheres exert on each other, what is the magnitude of the initial acceleration of the third sphere?
A 40 kg crate rests on a horizontal floor, and a 72 kg person is standing on the crate.
(a) Determine the magnitude of the normal force that the floor exerts on the crate.
(b) Determine the magnitude of the normal force that the crate exerts on the person.
The drawing shows a circus clown who weighs 785 N. The coefficient of static friction between the clown's feet and the ground is 0.48. He pulls vertically downward on a rope that passes around three pulleys and is tied around his feet. What is the minimum pulling force that the clown must exert to yank his feet out from under himself?
A box is sliding up an incline that makes an angle of 18.0° with respect to the horizontal. The coefficient of kinetic friction between the box and the surface of the incline is 0.180. The initial speed of the box at the bottom of the incline is 1.70 m/s. How far does the box travel along the incline before coming to rest?
sorry i've just been trying to figure them out but managed nothing.. hope you can help
did you ever figure out the one about the uniform spheres? i have the same problem for homework
A bucket of mass M = [05] kg is attached to a
second bucket of mass m = 3:52 kg by an ideal string. The
string is hung over an ideal pulley as shown in the �gure.
Mass M is started with an initial downward speed of
2.13 m/s. What then is the speed (m/s) of mass M after it
has moved 2.47 meters?
Of course, I'd be happy to help you with your homework questions! I'll explain how to solve each problem step by step. Let's start with the first question:
1. For the first question about the maximum gravitational force between the bowling ball and the billiard ball, you can use the formula for the magnitude of gravitational force between two objects: F = G * (m1 * m2) / r^2.
Here's how to calculate it:
- Given mass of the bowling ball (m1) = 7.2 kg, mass of the billiard ball (m2) = 0.41 kg, radius of the bowling ball (r1) = 0.12 m, and radius of the billiard ball (r2) = 0.028 m.
- The gravitational constant (G) = 6.67430 × 10^-11 m^3/(kg * s^2).
Using the formula, plug in the values to calculate the gravitational force:
F = (6.67430 × 10^-11) * [(7.2 * 0.41) / (0.12 + 0.028)^2]
Simplifying the equation will give you the magnitude of the maximum gravitational force between the two balls.
Now, let's move on to the second question:
2. For the second question about the initial acceleration of the third sphere in the equilateral triangle, you need to consider the gravitational forces between the spheres. The net force on the third sphere will determine its acceleration.
Here's how to calculate it:
- Given the masses of the two spheres at the corners (m1 = m2 = 3.20 kg) and the length of each side of the triangle (1.50 m).
- Assume the unknown mass of the third sphere is represented by m3, and the distance between the spheres is represented by R.
Using the formula for the magnitude of gravitational force between two objects, the net force on the third sphere can be calculated as:
F = G * [(m1 * m3) / R^2] + G * [(m2 * m3) / R^2]
Since the spheres form an equilateral triangle, the distance between any two spheres is the side length of the triangle.
Calculating the net force, you can use F = m3 * a, where 'a' is the acceleration.
Simplifying the equation will give you the magnitude of the initial acceleration of the third sphere.
Now, let's proceed to the third question:
3. For the third question regarding the normal forces between the crate and the person, you can start by considering Newton's third law of motion. According to this law, the force exerted by one object on another is equal in magnitude and opposite in direction.
(a) To calculate the magnitude of the normal force that the floor exerts on the crate, you need to consider the weight of both the crate and the person standing on it. The normal force will be equal to the sum of these weights.
(b) To determine the magnitude of the normal force that the crate exerts on the person, you can consider the crate as an object pressing against the person with an equal and opposite force (Newton's third law).
Now, let's move on to the fourth question:
4. For the fourth question concerning the minimum pulling force that the clown must exert to yank his feet out from under himself, you need to consider the static friction between the clown's feet and the ground.
- Given the weight of the clown (785 N) and the coefficient of static friction (0.48), you can calculate the maximum static friction force that can be exerted on the clown using F = μ * N, where μ is the coefficient of static friction and N is the normal force.
- This maximum static friction force will represent the minimum pulling force required to overcome it and yank the clown's feet out from under himself.
Lastly, let's address the fifth and final question:
5. For the fifth question about the box sliding up an incline and coming to rest, you need to consider the forces acting on the box. These forces include the component of weight along the incline and the force of kinetic friction.
- Given the angle of the incline (18.0°), the coefficient of kinetic friction (0.180), and the initial speed of the box (1.70 m/s), you can determine the initial kinetic energy of the box.
- As the box slides up the incline, work is done against the force of kinetic friction, causing a decrease in the box's kinetic energy.
- When the box comes to rest, all the initial kinetic energy is converted to other forms, such as potential energy and thermal energy due to friction.
- Using energy conservation principles, you can find the distance the box travels along the incline before coming to rest.
Follow these steps for each question, and you should be able to find the answers. Let me know if you need further assistance with any of these problems!