contestada

A 1.5 kg block is connected by a rope across a 50-cm-diameter, 2.0 kg , pulley that spins on a frictionless axle, as shown in (Figure 1). A constant 10 N tension is applied to the other end of the rope. Starting from rest, how long does it take the block to move 30 cm ?

A 15 kg block is connected by a rope across a 50cmdiameter 20 kg pulley that spins on a frictionless axle as shown in Figure 1 A constant 10 N tension is applie class=

Respuesta :

The time it takes the block to move 30cm is 0.56 seconds

Data;

  • Mass = 1.5kg
  • Diameter = 50cm
  • Tension = 10N
  • Distance moved = 30cm

The Force balance on vertical direction

T - mg = ma

T - 1.5g = 15a ...equation(i)

Using torque balance from center of pulley

[tex]\tau _n_e_t= FR-TR\\I\alpha =FR-TR[/tex]

where

I = moment of inertia about center = 1/2MR^2

[tex]\alpha =a/r[/tex]

Substitute the values into the equation

[tex](\frac{1}{2}*2.0*0.5^2) *\frac{1}{2}a= \frac{1}{2}*10-\frac{1}{2} *1.5*9.81 -\frac{1}{2} a*1.5\\0.75a+0.50a=-2.3575\\a=-1.9m/s^2[/tex]

The block moves backward since the acceleration is negative.

From the second equation of motion

[tex]S=ut+\frac{1}{2}at^2\\u=0\\t=?\\s=0.3\\0.3=0*t+\frac{1}{2}(1.90)t^2\\t=\sqrt{\frac{2.0*0.30}{1.90} }\\ t = 0.56s[/tex]

The time it takes the block to move 30cm is 0.56 seconds

Learn more about force on axle here;

https://brainly.com/question/7020147

Otras preguntas