Question

A 30 newton force is applied to an object at an angle of 30° above horizontal. If the object is moved a distance of 10 meters

horizontally along a frictionless surface using this force, what amount of kinetic energy is gained by the object?

Answer 1

The force applied to the object can be resolved into two components: a horizontal component and a vertical component. The horizontal component of the force is given by:

```
F_horizontal = F * cos(theta)
```

where F is the magnitude of the force (30 N) and theta is the angle above horizontal (30 degrees). Plugging in the values we get:

```
F_horizontal = 30 N * cos(30 degrees) = 25.98 N
```

Since the surface is frictionless, no work is done against friction. The work done by the force is equal to the change in kinetic energy of the object:

```
W = ΔK
```

The work done by the force is given by:

```
W = F_horizontal * d
```

where d is the distance moved horizontally by the object (10 m). Plugging in the values we get:

```
W = 25.98 N * 10 m = 259.8 J
```

Therefore, the object gains 259.8 joules of kinetic energy.