A block of mass 2 kg is resting on a smooth surface. At what angle a force of 10 N be acting on the block so that it will acquire a kinetic energy of 10 J after moving 2 m

Options

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

Explanation

To solve the problem step by step, we will use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.

### Step 1: Understand the Given Data
- Mass of the block (m) = 2 kg
- Force applied (F) = 10 N
- Distance moved (d) = 2 m
- Final kinetic energy (KE_final) = 10 J
- Initial kinetic energy (KE_initial) = 0 J (since the block is at rest)

### Step 2: Apply the Work-Energy Theorem
According to the work-energy theorem:
\[ \text{Work done} = \Delta KE = KE_{\text{final}} - KE_{\text{initial}} \]
Substituting the values:
\[ \text{Work done} = 10 J - 0 J = 10 J \]

### Step 3: Calculate the Work Done by the Applied Force
The work done by the applied force can be expressed as:
\[ \text{Work done} = F \cdot d \cdot \cos(\theta) \]
Where:
- \( F \) is the force applied (10 N)
- \( d \) is the distance moved (2 m)
- \( \theta \) is the angle between the force and the direction of displacement

Substituting the known values:
\[ 10 J = 10 N \cdot 2 m \cdot \cos(\theta) \]

### Step 4: Simplify the Equation
\[ 10 J = 20 N \cdot m \cdot \cos(\theta) \]
Dividing both sides by 20:
\[ \cos(\theta) = \frac{10 J}{20 N \cdot m} = \frac{1}{2} \]

### Step 5: Find the Angle
The cosine of the angle is given by:
\[ \cos(\theta) = \frac{1}{2} \]
This corresponds to:
\[ \theta = 60^\circ \]

### Final Answer
The angle at which the force of 10 N should be applied to achieve a kinetic energy of 10 J after moving 2 m is **60 degrees**.

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