v1f = -0.16 ms
Explanation:
Use the conservation law of linear momentum:
m1v1i + m2v2i = m1v1f + m2v2f
where
v1i = v2i = 0
m1 = 160 kg
m2 = 0.50 kg
v2f = 50m/s
v1f = ?
So we have
0 = (160 kg)v1f + (0.5 kg)(50 m/s)
v1f = -(25 kg-m/s)/(160 kg)
= -0.16 m/s
Note: the negative sign means that its direction is opposite that of the arrow.
Answer:
Explanation:
Conceptual analysis
To solve this problem we apply Newton's second law:
The acceleration of an object is proportional to the force F acting on it and inversely proportional to its mass m.
a = F / m
Where,
F = m * a Formula (1)
F: Force in Newtons (N)
m: mass in kg
a: acceleration in m/(s^2)
a = v / t Formula (2)
v: speed in m/s
t: time in seconds (s)
Known information
We know the following data:
m = 1kg
v = 1 m/s
t = 1s
Development of the problem:
In the Formula (2): 
In the Formula (1): 
Answer: 55 ohms
Explanation:
Given that,
Voltage of heater (v) = 110-volt
Current drawn by heater (I) = 2.0 amperes
resistance of the heater (r) = ?
Since voltage, current and resistance are involved, apply the formula for ohms law.
Voltage = current x resistance
i.e v = ir
where r = v / i
r = 110 volts / 2.0 A
r = 55 ohms
Thus, the resistance of the heater is 55 ohms
Explanation:
By the statement, Efficiency of a machine is 60% it is meant that 'The work output is 60% of the work input'. If you apply 100J of energy for a machine, it will be able to life load of 60 J only
Answer:
Explanation:
Let the tension in the cord be T₁ and T₂ .
for motion of block placed on horizontal table
T₁ = m a , a is acceleration of the whole system .
for motion of hanging bucket of mass m
mg - T₂ = ma
adding the two equation
mg + T₁- T₂ = 2ma
for rotational motion of the pulley
torque = moment of inertia x angular acceleration
(T₂ - T₁) R = I x α , I is moment of inertia of pulley , α is angular acceleration .
(mg - 2ma ) R = I x α
(mg - 2ma ) R = I x a / R
(mg - 2ma ) R² = I x a
mgR² = 2ma R² + I x a
a = mgR² / (2m R² + I )
Since body moves by distance d in time T
d = 1/2 a T²
a = 2d / T²
mgR² / (2m R² + I ) = 2d / T²
mgR²T² = 2d x (2m R² + I )
mgR²T² - 4dm R² = 2dI
m R² ( gT² - 4d ) = 2dI
I = m R² ( gT² - 4d ) ] / 2d .
