Starting from rest, a 5kg block slides 2.5 m down a rough 30o incline in 2 seconds. Find
a) the work done by the force of gravity.
b) the work done by friction.
c) the work done by the normal force
Help ASAP please!! Show work step by step only with the equation
Sure, let's calculate the work done in each case step by step using the appropriate equations.
a) The work done by the force of gravity can be calculated using the equation:
Work = Force x Distance x cos(angle)
In this case, the force of gravity can be calculated using the formula:
Force of gravity = mass x acceleration due to gravity
Here, the mass of the block is 5 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Plugging these values into the equation, we get:
Force of gravity = 5 kg x 9.8 m/s^2 = 49 N
Now, we need to find the component of this force along the direction of the incline. Since the incline makes an angle of 30 degrees with the horizontal, the cosine of this angle is cos(30) ≈ 0.866. Plugging this value into the equation, we get:
Work = 49 N x 2.5 m x 0.866 ≈ 106.42 J
Therefore, the work done by the force of gravity is approximately 106.42 J.
b) The work done by friction can be calculated using the equation:
Work = Force of friction x Distance x cos(angle)
To find the force of friction, we need to find the normal force first. The normal force is equal to the component of the weight perpendicular to the incline. Since the incline makes an angle of 30 degrees with the horizontal, the sine of this angle is sin(30) ≈ 0.5. Therefore, the normal force can be calculated as:
Normal force = Force of gravity x sin(angle)
Normal force = 49 N x 0.5 = 24.5 N
Now we can calculate the force of friction using the equation:
Force of friction = coefficient of friction x normal force
The coefficient of friction is not given in the question, so we cannot calculate the exact value of the force of friction without that information. However, we can write the equation for the work done by friction using the force of friction:
Work = Force of friction x Distance x cos(angle)
c) The work done by the normal force is equal to zero since the normal force is always perpendicular to the displacement. Therefore, the work done by the normal force is zero.
So, to summarize:
a) The work done by gravity is approximately 106.42 J.
b) The work done by friction cannot be calculated without the coefficient of friction.
c) The work done by the normal force is zero.
To find the work done by different forces, we need to calculate the work done by gravity, friction, and the normal force. Let's break it down step by step.
a) Work done by the force of gravity:
The work done by gravity can be calculated using the formula:
Work (W) = Force (F) * Distance (d) * cos(theta)
In this case, the force of gravity acting on the block can be calculated using the formula:
Force of gravity (F_gravity) = Mass (m) * Acceleration due to gravity (g)
Here, the mass of the block is given as 5 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, we can calculate the force of gravity:
F_gravity = 5 kg * 9.8 m/s^2 = 49 N
Now, we can calculate the work done by gravity using the given distance (d = 2.5 m) and the angle theta (30 degrees). However, we need to find the component of the force of gravity along the direction of motion. To do that, we need to find the weight component acting along the incline.
Weight component along the incline (F_weight) = F_gravity * sin(theta)
F_weight = 49 N * sin(30 degrees) = (49 N) * (0.5) = 24.5 N
Now, we can calculate the work done by gravity:
Work (W_gravity) = F_weight * d * cos(theta)
W_gravity = 24.5 N * 2.5 m * cos(30 degrees)
Using the cosine value of 30 degrees (0.866):
W_gravity = 24.5 N * 2.5 m * 0.866 = 52.9375 Joules
So, the work done by the force of gravity is approximately 52.9375 Joules.
b) Work done by friction:
The work done by friction can be determined using the equation:
Work (W_friction) = Force of friction (F_friction) * Distance (d)
To calculate the force of friction, we need to find the normal force acting on the block. The normal force can be calculated using:
Normal force (F_normal) = Mass (m) * Acceleration due to gravity (g) * cos(theta)
F_normal = 5 kg * 9.8 m/s^2 * cos(30 degrees)
Using the cosine value of 30 degrees (0.866):
F_normal = 5 kg * 9.8 m/s^2 * 0.866 = 42.427 N
Now, to calculate the frictional force, we need to consider that friction opposes the motion. Since the block is sliding down the incline, friction acts up the incline and is given by:
Force of friction (F_friction) = µ * F_normal
Here, µ is the coefficient of friction, which is not provided in the question. So we cannot directly calculate the work done by friction without knowing the coefficient. Let's assume a coefficient of friction of 0.3 for this example.
Force of friction (F_friction) = 0.3 * 42.427 N = 12.728 N
Now, we can calculate the work done by friction using the given distance (d = 2.5 m):
W_friction = F_friction * d = 12.728 N * 2.5 m = 31.82 Joules
So, the work done by the force of friction is approximately 31.82 Joules.
c) Work done by the normal force:
The work done by the normal force is zero because the normal force acts perpendicular to the direction of motion. Therefore, no work is done by the normal force.
To summarize:
a) The work done by the force of gravity is approximately 52.9375 Joules.
b) The work done by the force of friction is approximately 31.82 Joules.
c) The work done by the normal force is zero.
Please note that the values mentioned for the coefficient of friction and angle are assumed in this explanation, as they were not provided in the question. It's essential to use the correct values if they are given.