A 0.55 kg block slides across a tabletop with initial velocity of 3 m/s and it comes to rest in a distance of 0.53 m. Find the average friction force that ed its motion.
Wb = mg = 0.55kg * 9.8N/kg = 5.39N.
Fb = (5.39N.,0 deg.).
Fp = Fh = 5.39sin(0) = 0 = Force parallel to plane = Hor. comp.
Ff = Force due to friction.
a = (Vf^2 - V9^2) / 2d,
a = (0 - (3^2)) / 1.06 = -8.49m/s^2.
Fn = ma = 0.55 * (-8.49) = -4.67N. = Net force.
Fn = Fp - Ff = -4.67,
0 - Ff = -4.67,
Ff = 4.67N = Force due to friction.
To find the average friction force that ed the motion of the block, we can use the formula:
Force of friction = Mass * Acceleration
First, we need to find the acceleration of the block. We can use one of the kinematic equations to find it. The equation that relates initial velocity (v₀), final velocity (v), acceleration (a), and distance (d) is:
v² = v₀² + 2ad
Rearranging the equation, we have:
a = (v² - v₀²) / (2d)
Now, let's plug in the values given:
v₀ = 3 m/s
v = 0 m/s (since the block comes to rest)
d = 0.53 m
Substituting these values into the equation, we can calculate the acceleration (a):
a = (0² - 3²) / (2 * 0.53)
a = (-9) / 1.06
a ≈ -8.49 m/s²
Next, we can find the average friction force by multiplying the mass of the block by the acceleration:
m = 0.55 kg (given)
Force of friction = m * a
Force of friction = 0.55 kg * (-8.49 m/s²)
Calculating the result:
Force of friction ≈ -4.67 N
The negative sign indicates that the friction force acts in the opposite direction to the initial motion of the block, effectively retarding its motion.