A force of 100 N displacement an object through 0.2 m and does work of 10 joules. What is the angle between the force and displacement?

Options

A. `30^(@)`
B. `60^(@)`
C. `45^(@)`
D. `90^(@)`

Explanation

To solve the problem step by step, we need to find the angle between the force and the displacement given the work done, force, and displacement.

### Step 1: Understand the Work Done Formula
The work done (W) by a force (F) when it moves an object through a displacement (s) at an angle (θ) is given by the formula:
\[ W = F \cdot s \cdot \cos(\theta) \]

### Step 2: Identify the Given Values
From the problem, we have:
- Work done, \( W = 10 \) joules
- Force, \( F = 100 \) N
- Displacement, \( s = 0.2 \) m

### Step 3: Substitute the Known Values into the Formula
We can substitute the known values into the work done formula:
\[ 10 = 100 \cdot 0.2 \cdot \cos(\theta) \]

### Step 4: Calculate the Product of Force and Displacement
Calculate \( 100 \cdot 0.2 \):
\[ 100 \cdot 0.2 = 20 \]
So, we can rewrite the equation as:
\[ 10 = 20 \cdot \cos(\theta) \]

### Step 5: Isolate \( \cos(\theta) \)
To find \( \cos(\theta) \), we can rearrange the equation:
\[ \cos(\theta) = \frac{10}{20} \]
\[ \cos(\theta) = 0.5 \]

### Step 6: Find the Angle \( \theta \)
Now, we need to find the angle whose cosine is 0.5. This can be done using the inverse cosine function:
\[ \theta = \cos^{-1}(0.5) \]

### Step 7: Determine the Value of \( \theta \)
From trigonometric values, we know:
\[ \cos(60^\circ) = 0.5 \]
Thus,
\[ \theta = 60^\circ \]

### Final Answer
The angle between the force and the displacement is:
\[ \theta = 60^\circ \]

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