A 8 kg object is pulled along a horizontal surface at a constant speed by a 30 N force acting 60 degrees above the horizontal.
How much work is done by the force as the object moves 7 m?
horzontal force*distance=30*cos60*7=15*7= .... work done in joules
To find the work done by the force, we can use the formula:
work = force * displacement * cos(theta)
Where:
- force is the magnitude of the force applied (30 N)
- displacement is the distance the object moves (7 m)
- theta is the angle between the force and the displacement (60 degrees)
Plugging in the values, we have:
work = 30 N * 7 m * cos(60 degrees)
To evaluate cos(60 degrees), we know that in a 30-60-90 right triangle, the cosine of 60 degrees is 1/2.
work = 30 N * 7 m * (1/2) = 105 Nm
Therefore, the work done by the force as the object moves 7 m is 105 Joules (J).
To calculate the amount of work done by a force, you can use the formula:
Work = Force * Distance * cos(θ)
Where:
- Work is the amount of work done in joules (J).
- Force is the magnitude of the force in newtons (N).
- Distance is the displacement of the object in meters (m).
- θ is the angle between the force and the direction of displacement in degrees.
In this case, the force is 30 N, the distance is 7 m, and the angle θ is 60 degrees.
First, you need to calculate the horizontal component of the force since the object is being pulled horizontally. The horizontal component can be found using the formula:
Horizontal Component = Force * cos(θ)
So, the horizontal component of the force is:
Horizontal Component = 30 N * cos(60°) = 30 N * 0.5 = 15 N
Now, you can calculate the amount of work done:
Work = (Horizontal Component) * Distance * cos(0°)
Since cos(0°) = 1, the formula simplifies to:
Work = (Horizontal Component) * Distance
Plugging in the values:
Work = 15 N * 7 m = 105 J
Therefore, the work done by the force as the object moves 7 m is 105 joules.