A 200 N box is pushed up an incline 10 m long and 3 m high. The average force (parallel to the plane) is 120 N.
a.) How much work is done?
b.) What is the change in the PE of the box?
c.) What is the change in KE of the box?
d.) What is the frictional force on the box?
Wb = M*g = 200 N., M = 200/g = 200/9.8 =
20.4 kg.
sin A = 3/10 = 0.30, A = 17.5o.
Fp = 200*sin17.5 = 60 N.
Fn = 200*Cos17.5 = 191 N.
a. Work = F*d = 120 * 10 = 1200 J.
b. Mg*h-0 = Mg*h = 200 * 3 = 600 J.
c. Conservation Energy : Change in KE =
Change in PE = 600 J.
d. Fap-Fp-Fk = M*a.
120-60-Fk = M*0 = 0.
Fk = 120-60 = 60 N.
Roger pushes a box on a 30° incline. If he applies a force of 60 newtons parallel to the incline and displaces the box 10 meters along the incline, how much work will he do on the box?
To solve these problems, we can use the formulas related to work, potential energy, kinetic energy, and the frictional force.
a.) How much work is done?
The work done is given by the formula:
Work = Force * Distance * cos(theta)
Where:
- Force is the average force parallel to the plane (120 N)
- Distance is the length of the incline (10 m)
- cos(theta) is the cosine of the angle between the force and the displacement (which is the same as the angle of the incline, given by the ratio of the height to the length)
Since the angle of the incline is given by the ratio of the height to the length (3 m / 10 m), we can calculate cos(theta) as follows:
cos(theta) = adjacent side / hypotenuse
= 10 m / sqrt[(10 m)^2 + (3 m)^2]
= 10 m / sqrt[100 m^2 + 9 m^2]
= 10 m / sqrt[109 m^2]
= 10 m / 10.44 m
≈ 0.956
Now we can calculate the work done:
Work = 120 N * 10 m * 0.956
= 1,147.2 J
Therefore, the work done is approximately 1,147.2 Joules.
b.) What is the change in the PE of the box?
The change in potential energy is given by the formula:
Change in PE = m * g * h
Where:
- m is the mass of the box (which can be calculated using Newton's second law, F = m * a)
- g is the acceleration due to gravity (assumed to be 9.8 m/s^2)
- h is the height of the incline (3 m)
To find the mass of the box, we can use Newton's second law:
Force = mass * acceleration
In this case, the force is given (200 N) and the acceleration is the acceleration due to gravity (9.8 m/s^2).
So, we can calculate the mass:
200 N = mass * 9.8 m/s^2
mass = 200 N / 9.8 m/s^2
mass ≈ 20.41 kg
Now we can calculate the change in potential energy:
Change in PE = 20.41 kg * 9.8 m/s^2 * 3 m
≈ 598.1 J
Therefore, the change in potential energy is approximately 598.1 Joules.
c.) What is the change in KE of the box?
The change in kinetic energy is given by the formula:
Change in KE = Work - Change in PE
Using the values we have already calculated:
Change in KE = 1,147.2 J - 598.1 J
= 549.1 J
Therefore, the change in kinetic energy is 549.1 Joules.
d.) What is the frictional force on the box?
To find the frictional force on the box, we need to use the equation:
Force of friction = Force applied - Force parallel to the plane
In this case, the force applied is given (200 N) and the force parallel to the plane is given (120 N).
So, the frictional force is:
Force of friction = 200 N - 120 N
= 80 N
Therefore, the frictional force on the box is 80 Newtons.
To solve this problem, we'll need to use some concepts from physics, specifically work, potential energy, kinetic energy, and friction.
a.) How much work is done?
The work done can be calculated using the formula: work = force × distance × cosine(theta), where theta is the angle between the force and the displacement. In this case, the force is given as 120 N and the distance is 10 m. Since the force is applied parallel to the incline, the angle between force and displacement is 0 degrees. Thus, the work done is:
work = 120 N × 10 m × cos(0°) = 1200 J
So, the work done is 1200 Joules.
b.) What is the change in the PE of the box?
To find the change in potential energy, we can use the formula: potential energy = mass × gravity × height. In this case, the force applied parallel to the incline is responsible for the change in potential energy. The height is given as 3 m, and since the force is parallel to the incline, it directly opposes the gravitational force acting on the box. Therefore, the change in potential energy can be calculated by:
potential energy = force × height = 120 N × 3 m = 360 J
So, the change in potential energy of the box is 360 Joules.
c.) What is the change in KE of the box?
The change in kinetic energy can be calculated by subtracting the initial kinetic energy from the final kinetic energy. However, we need to find the initial kinetic energy first. Since the box is initially at rest, the initial kinetic energy is zero. The final kinetic energy can be calculated using the formula: kinetic energy = 0.5 × mass × velocity^2.
Since we don't have the mass or velocity given directly, we'll need to use some more information. The work done on the box is equal to the change in kinetic energy. So, we can equate the work done to the final kinetic energy:
work = kinetic energy
1200 J = 0.5 × mass × velocity^2
Unfortunately, we don't have enough information to directly calculate the change in kinetic energy without knowing either the mass or the velocity of the box.
d.) What is the frictional force on the box?
The frictional force can be determined using the equation: frictional force = force parallel - force opposing. In this case, the force opposing is the force due to gravity acting in the downward direction along the incline.
force opposing = mass × gravity × sin(theta)
Since we don't have the mass given, we can't calculate the frictional force without further information.