A 0.50 kg block initially at rest on a frictionless horizontal surface is acted upon by a force of 8.0 N for a distance of 7.5 m. What is the velocity of the block in m/s?
A 150-L water heater is rated at 8 kW. If 20 percent of its heat escapes, how long does the heater take to raise the temperature of 150 L of water from 10 oC to 60 oC?
To find the velocity of the block, you can use Newton's second law of motion, which states that the force applied to an object is equal to its mass multiplied by its acceleration.
1. First, calculate the acceleration of the block using the formula:
F = m * a
Where:
F = force applied to the block = 8.0 N
m = mass of the block = 0.50 kg
a = acceleration of the block (to be determined)
Rearranging the formula, we have:
a = F / m
Substituting the given values:
a = 8.0 N / 0.50 kg
a = 16.0 m/s^2
The block's acceleration is 16.0 m/s^2.
2. Next, you can use the kinematic equation to find the final velocity of the block:
v^2 = u^2 + 2a * s
Where:
v = final velocity of the block (to be determined)
u = initial velocity of the block (which is 0 as the block is initially at rest)
a = acceleration of the block (which is 16.0 m/s^2)
s = distance traveled by the block = 7.5 m
Rearranging the equation, we have:
v^2 = 0 + 2 * 16.0 m/s^2 * 7.5 m
v^2 = 240 m^2/s^2
Taking the square root of both sides:
v = sqrt(240) m/s
v ≈ 15.49 m/s
Therefore, the velocity of the block is approximately 15.49 m/s.
To find the velocity of the block, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
Here's how to calculate the velocity of the block step by step:
1. Calculate the acceleration of the block using Newton's second law:
Force (F) = mass (m) × acceleration (a)
Rearranging the equation, we have:
acceleration (a) = Force (F) / mass (m)
Plugging in the values given, we have:
a = 8.0 N / 0.50 kg
a = 16.0 m/s^2
2. Determine the distance traveled by the block (d) using the given value:
d = 7.5 m
3. Use the equation of motion to calculate the final velocity (vf) of the block:
vf^2 = vi^2 + 2ad
Since the block is initially at rest (vi = 0), the equation simplifies to:
vf^2 = 2ad
Plugging in the values, we have:
vf^2 = 2 × 16.0 m/s^2 × 7.5 m
vf^2 = 240 m^2/s^2
Taking the square root of both sides, we find:
vf = √(240) m/s
vf ≈ 15.49 m/s
Therefore, the velocity of the block is approximately 15.49 m/s.
If the movement is in the direction of the force,
KEblock=workputin
1/2 m v^2=8N*7.5m
solve for v