Answer:
a) a = 0.477 m/s^2
b) u = 0.04862
Explanation:
Given:-
- The rotational speed of the turntable N = 33 rev/min
- The watermelon seed is r = 4.0 cm away from axis of rotation.
Find:-
(a) Calculate the acceleration of the seed, assuming that it does not slip. (b) What is the minimum value of the coefficient of static friction between the seed and the turntable if the seed is not to slip
Solution:-
- First determine the angular speed (w) of the turntable.
w = 2π*N / 60
w = 2π*33 / 60
w = 3.456 rad/s
- The watermelon seed undergoes a centripetal acceleration ( α ) defined by:
α = w^2 * r
α = 3.456^2 * 0.04
α = 0.477 m / s^2
- The minimum friction force (Ff) is proportional to the contact force of the seed.
- The weight (W) of the seed with mass m acts downwards. The contact force (N) can be determined from static condition of seed in vertical direction.
N - W = 0
N = W = m*g
- The friction force of the (Ff) is directed towards the center of axis of rotation, while the centripetal force acts in opposite direction. The frictional force Ff = u*N = u*m*g must be enough to match the centripetal force exerted by the turntable on the seed.
Ff = m*a
u*m*g = m*a
u = a / g
u = 0.477 / 9.81
u = 0.04862
Question: A loader sack of total mass
is l000 grams falls down from
the floor of a lorry 200 cm high
Calculate the workdone by the
gravity of the load.
Answer:
19.6 Joules
Explanation:
Applying
W = mgh........................ Equation 1
Where W = Workdone by gravity on the load, m = mass of the loader sack, h = height, g = acceleration due to gravity
From the question,
Given: m = 1000 grams = (1000/1000) kilogram = 1 kg, h = 200 cm = 2 m
Constant: g = 9.8 m/s²
Substitute these values into equation 1
W = (1×2×9.8)
W = 19.6 Joules
Hence the work done by gravity on the load is 19.6 Joules
Answer:
v=32.49 m/s
Explanation:
Given that
Distance ,d= 66 m
Initial speed of the car ,u = 0 m/s
Coefficient of friction ,μ = 0.8
Lets take the total mass of the car = m
The acceleration of the car is given as
a = μ g ( g= 10 m/s² )
Now by putting the values in the above equation we get
a= 0.8 x 10 m/s²
a= 8 m/s²
We know that ,final speed is given as
v²= u ²+ 2 a d
Now putting the value
v²=0² + 2 x 8 x 66
v²= 1056
v=32.49 m/s
We know the formula for density = Mass/ volume
So Mass, M = Volume * Density
Volume = 3.5 L= 0.0035
Density = 1.50 g/ml = 1500
Mass, M = 0.0035*1500 = 5.25 kg
So mass of liquid having density 1.50 g/ml and volume 3.5 liters is 5.25 kg.