A constant force of 58.3 N, directed at 31.7 degrees form horizontal, pulls a mass of 11.9 kg horizontally a distance of 2.77 m. Calculate the work done by the force.
is the force upwards, or downward.
Assuming upwards.
vertical component= 58.3sin31.7
horizontal pulling component=58.3cos31.7
work done= force*distance
58.3cos31.7*2.77
work done in the vertical
58.3*sin31.7*zero
To calculate the work done by the force, we can use the formula:
Work = Force * Distance * cos(theta)
Where:
- Work is the work done by the force (in joules)
- Force is the constant force (in newtons)
- Distance is the distance over which the force is applied (in meters)
- theta is the angle between the force and the direction of motion (in degrees)
Given:
Force = 58.3 N
Distance = 2.77 m
theta = 31.7 degrees
First, we need to convert the angle from degrees to radians.
1 degree = π/180 radians
theta (in radians) = 31.7 * π/180
Now we can calculate the work:
Work = 58.3 N * 2.77 m * cos(31.7 * π/180)
Calculating this expression will give us the work done by the force.
To calculate the work done by the force, we can use the formula:
Work = Force x Distance x cos(theta)
Where:
- Work is the amount of energy transferred by the force, measured in joules (J).
- Force is the magnitude of the force applied, measured in newtons (N).
- Distance is the displacement caused by the force, measured in meters (m).
- theta (θ) is the angle between the force vector and the displacement vector.
In this case, we are given:
- Force = 58.3 N
- Distance = 2.77 m
- theta (θ) = 31.7 degrees
First, we need to convert the angle from degrees to radians, since the cosine function in the formula expects the angle to be in radians. To convert degrees to radians, we use the formula:
radians = degrees x (π/180)
Therefore, in radians, theta (θ) = 31.7 x (π/180)
Once we have the angle in radians, we can calculate the work done:
Work = 58.3 N x 2.77 m x cos(31.7 x (π/180))
Now we can evaluate this expression to find the work done.