A small mass slides without friction across a plane an (x,y) coordinate system directly from the origin to a point with (x,y) coordinates (1.3 m, 9.6 m); a constant force acts on it. The force has magnitude 2.1 N and its direction is at a counterclockwise angle of 128o from the positive x axis. How much work is done by the force on the mass during the displacement?

Do I use F*d*cos(theta) or just F*d?

F*d

unsw phys1121 reppin

To calculate the work done by a force on an object during a displacement, you need to use the formula W = F * d * cos(theta), where W represents the work done, F is the magnitude of the force, d is the magnitude of the displacement, and theta is the angle between the force and the displacement.

In this case, you are given the magnitude of the force (2.1 N) and the angle between the force and the positive x-axis (128 degrees counterclockwise). You also have the displacement, which is the distance between the origin (0,0) and the point (1.3 m, 9.6 m).

Since you want to find the work done by the force, you can directly plug in the given values into the formula: W = F * d * cos(theta).

Using the given values:
- F = 2.1 N
- d = sqrt((1.3 m)^2 + (9.6 m)^2) = 9.71 m (distance formula)
- theta = 128 degrees

Now, substitute these values into the formula to find the work done:
W = 2.1 N * 9.71 m * cos(128 degrees)

To use the formula correctly, you need to convert the angle from degrees to radians since the cosine function in the formula uses radians. To convert degrees to radians, use the formula: radians = degrees * pi / 180.

Converting 128 degrees to radians:
theta_radians = 128 * pi / 180

Now, you can calculate the work done:
W = 2.1 N * 9.71 m * cos(theta_radians)

Evaluate this expression using a calculator to find the work done by the force on the mass during the displacement.