A box of mass 5 kg is pulled along a horizontal frictionless surface by a force of 40N inclined @ 30dgrees. Calculate A)the work done by the force over a distance. B)the speed gained by the box after travelling 10m.
The force component in the direction of motion is 40 cos30 N = 34.64 N
A) 34.64 N * distance
(You left out the distance)
B) Set the work done over 10 m equal to final kinetic energy and solve for V.
To solve this problem, we need to use some basic principles of physics and equations related to work and energy.
A) To calculate the work done by the force, we can use the formula:
Work (W) = Force (F) * Distance (d) * cosine(theta)
Where:
- Work (W) is the energy transferred to or from an object by means of a force acting on the object.
- Force (F) is the applied force.
- Distance (d) is the distance over which the force is applied.
- theta (θ) is the angle between the direction of the force and the direction of motion.
In this case, the force is 40N, and since it is inclined at an angle of 30 degrees, we need to find the component of this force acting parallel to the direction of motion. This component is given by:
Force parallel (F_parallel) = Force (F) * cosine(theta)
So, F_parallel = 40N * cos(30°) = 40N * (sqrt(3)/2) = 40N * 0.866 = 34.64N
Now, we can calculate the work done by this force over a distance using the formula:
Work (W) = Force parallel (F_parallel) * Distance (d)
Given the force (F_parallel) of 34.64N and the distance (d), you can substitute them into the equation to find the value of work (W in Joules).
B) To calculate the speed gained by the box after traveling a distance of 10m, we can relate the work done to the kinetic energy gained by the box.
The work done is given by:
Work (W) = Change in kinetic energy (ΔKE)
And the formula for kinetic energy is:
Kinetic energy (KE) = 0.5 * mass * velocity^2
We are given the mass of the box as 5 kg. Initially, the box is at rest, so its initial kinetic energy (KE_initial) is zero.
The work done (W) is the change in kinetic energy (ΔKE), which is given by:
W = KE_final - KE_initial
Since KE_initial is zero, we have:
W = KE_final - 0
W = KE_final
Now, we can equate the work done to the change in kinetic energy:
KE_final = W
Since the work done (W) is already calculated in part A, you can substitute this value into the equation to find the final kinetic energy of the box. Finally, we can determine the speed gained by the box using the formula for kinetic energy mentioned earlier.