A block with mass (m = 19.5 kg) is pulled with a force (F = 280 N) 0 = 25°. a) Draw a free-body diagram. ) Find the normal force. c) If coefficient of friction between the crate and the surface is uk=0.12, what is the value of the frictional force,fr. d) Find the acceleration. e) What minimum horizontal force is needed to move the block with a constant speed (while keeping the F = 280 N)? F
A block with mass (m = 19.5 kg) is pulled with a force (F = 280 N) 0 = 25°. a) Draw a free-body diagram. ) Find the normal force. c) If coefficient of friction between the crate and the surface is uk=0.12, what is the value of the frictional force,fr. d) Find the acceleration. e) What minimum horizontal force is needed to move the block with a constant speed (while keeping the F = 280 N)? F
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![**Physics Problem: Block Moving on a Surface**
**Problem Statement**
A block with mass \( m = 19.5 \) kg is pulled with a force \( F = 280 \) N at an angle \( \theta = 25° \).
**Questions**
a) Draw a free-body diagram.
b) Find the normal force.
c) If the coefficient of friction between the crate and the surface is \( \mu_k = 0.12 \), what is the value of the frictional force, \( f_k \)?
d) Find the acceleration.
e) What minimum horizontal force is needed to move the block with a constant speed (while keeping \( F = 280 \) N)?
**Free-Body Diagram Explanation**
The diagram included shows a block on a horizontal surface. The block has mass \( m \) and a force \( F \) is applied at an angle \( \theta \) above the horizontal. The components of the force \( F \) are split into horizontal and vertical components relative to the block:
- \( F \cos(\theta) \) acting horizontally
- \( F \sin(\theta) \) acting vertically upwards
Additionally, there are two other forces acting on the block:
- Gravitational force \( mg \) acting downwards
- Normal force \( N \) acting perpendicular to the surface and upwards
**Equations and Calculations**
1. **Normal Force (b):**
\[
N = mg - F \sin(\theta)
\]
2. **Frictional Force (c):**
\[
f_k = \mu_k \cdot N
\]
3. **Acceleration (d):**
\[
\text{Net force} = F \cos(\theta) - f_k
\]
\[
a = \frac{\text{Net force}}{m}
\]
4. **Minimum Horizontal Force for Constant Speed (e):**
For constant speed, Net force \( = 0 \):
\[
F \cos(\theta) = f_k
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae88911f-9dac-42fc-844f-67ccf125de46%2Fe1f83ec2-add9-4eff-8559-35d37078b19b%2Fkv6726_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Physics Problem: Block Moving on a Surface**
**Problem Statement**
A block with mass \( m = 19.5 \) kg is pulled with a force \( F = 280 \) N at an angle \( \theta = 25° \).
**Questions**
a) Draw a free-body diagram.
b) Find the normal force.
c) If the coefficient of friction between the crate and the surface is \( \mu_k = 0.12 \), what is the value of the frictional force, \( f_k \)?
d) Find the acceleration.
e) What minimum horizontal force is needed to move the block with a constant speed (while keeping \( F = 280 \) N)?
**Free-Body Diagram Explanation**
The diagram included shows a block on a horizontal surface. The block has mass \( m \) and a force \( F \) is applied at an angle \( \theta \) above the horizontal. The components of the force \( F \) are split into horizontal and vertical components relative to the block:
- \( F \cos(\theta) \) acting horizontally
- \( F \sin(\theta) \) acting vertically upwards
Additionally, there are two other forces acting on the block:
- Gravitational force \( mg \) acting downwards
- Normal force \( N \) acting perpendicular to the surface and upwards
**Equations and Calculations**
1. **Normal Force (b):**
\[
N = mg - F \sin(\theta)
\]
2. **Frictional Force (c):**
\[
f_k = \mu_k \cdot N
\]
3. **Acceleration (d):**
\[
\text{Net force} = F \cos(\theta) - f_k
\]
\[
a = \frac{\text{Net force}}{m}
\]
4. **Minimum Horizontal Force for Constant Speed (e):**
For constant speed, Net force \( = 0 \):
\[
F \cos(\theta) = f_k
\]
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